Weakly Reversible CF-Decompositions of Chemical Kinetic Systems

The paper proves that a PLK system with a weakly reversible PL‑RDK decomposition is weakly reversible and, under bi‑level independence with PLP‑type subnetworks (PE,i = S̃i), has a PLP log‑parametrization with PE = ∑ S̃i. This is stated and sketched in Proposition 7.12(i) (weak reversibility) and Theorem 7.17 (PLP parametrization), with the k=2 case shown directly and k>2 asserted by induction, and the intersection-of-equilibria step justified by independence (Feinberg’s decomposition theorem) . The candidate solution reaches the same conclusions but supplies a different, concise argument for nonemptiness of the multiway intersection by constructing a linear functional on S̃ and invoking Riesz representation to produce a point b whose translates hit all cosets simultaneously. Assumptions match the paper’s (weakly reversible PL‑RDK decomposition; independence; bi‑level independence; subnetworks of PLP type with PE,i=S̃i). Thus, both are correct; the proofs are materially different in the intersection step.